Announcements


There are no announcements

Forum

General


This course is part of the MAGIC core.

Description

This course is an introduction to set theory, focusing on foundational issues but with an eye also on the study of combinatorial properties of infinite objects.
We will start by motivating and introducing ZFC. Then we will develop the basic theory of the ordinals and cardinals in this theory, and will prove some classical theorems of combinatorial flavour. Possible topics may include cardinal arithmetic, Aronszajn trees, infinite Ramsey theory and/or some results on determinacy of games. Time permitting, I will briefly discuss large cardinal axioms, the independence phenomenon, and the problem of finding natural extensions of ZFC.
One of the goals of the course is to engage a working mathematician into looking at the foundations of the mathematical building.

Semester

Spring 2018 (Monday, January 22 to Friday, March 16; Monday, April 23 to Friday, May 4)

Timetable

  • Tue 12:05 - 12:55

Prerequisites

There are no prerequisites for this course, except for a reasonable level of mathematical maturity. Having been exposed to a course in mathematical logic would be desirable but not necessary. In fact I will give brief introductions to the relevant notions from logic.

Syllabus

Naive set theory: Sets as foundational framework for mathematics. Paradoxes.
Axiomatic set theory: ZFC.
Ordinals and cardinals. Transfinite recursion and induction. The cumulative hierarchy.
Countable and uncountable sets.
The Axiom of Choice.
Basic cardinal artihmetic.
Some combinatorial set theory: Aronszajn trees, infinite Ramsey theory.
Determinacy of infinite games.
Large cardinal axioms: Weakly compact, measurable, and beyond.
Natural axioms for mathematics: Extending ZFC.

Lecturer


David Aspero
Email d.aspero@uea.ac.uk
Phone +44 (0)1603 591433
Photo of David Aspero
Profile: I am a lecturer in Pure Mathematics at the School of Mathematics of the University of East Anglia. My work in mathematics is in set theory, and more specifically in infinite combinatorics, forcing, forcing axioms, large cadinals, definability issues, and the interactions between these areas.


Students


There are currently no students registered for this course.

Bibliography


Set theory: an introduction to independence proofsKenneth Kunen
Set Theory: The Third Millenium Edition, Revised and ExpandedThomas Jech
A mathematical introduction to logic (2nd. edition)Herbert Enderton


Note:

Clicking on the link for a book will take you to the relevant Google Book Search page. You may be able to preview the book there. On the right hand side you will see links to places where you can buy the book. There is also link marked 'Find this book in a library'. This sometimes works well, but not always. (You will need to enter your location, but it will be saved after you do that for the first time.)

Assessment



No assessment information is available yet.

No assignments have been set for this course.

Files



No files have yet been uploaded for this course.

Recorded Lectures


Please log in to view lecture recordings.